Question

[Hồ Huỳnh Anh]

trả lời câu hỏi nyaf giúp mik

Answer 1

[Member lỗi thời :>>]

Ta có :

\(\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{1}{a.\left(a+4\right)}=\frac{46}{945}\)

\(\Rightarrow\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{a.\left(a+4\right)}=\frac{23}{1890}\)

\(\Rightarrow\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{a}-\frac{1}{a+4}=\frac{23}{1890}\)

\(\Rightarrow\frac{1}{5}-\frac{1}{a+4}=\frac{23}{1890}\)

\(\Rightarrow\frac{1}{a+4}=\frac{1}{5}-\frac{23}{1890}=\frac{71}{378}\)

=> 71 . ( a + 4 ) = 378 

=> 71 . a + 284 = 378

=> 71 . a = 94

=> x = \(\frac{94}{71}\)

Answer 2

[Kun ( team ๖ۣۜƝƘ☆ )]

\(\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{1}{a.\left(a+4\right)}=\frac{46}{945}\)

\(\Leftrightarrow4.\left(\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{1}{a.\left(a+4\right)}\right)=\frac{46}{945}.4\)

\(\Leftrightarrow\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{a.\left(a+4\right)}=\frac{184}{945}\)

\(\Leftrightarrow\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+....+\frac{1}{a}-\frac{1}{a+4}=\frac{184}{945}\)

\(\Leftrightarrow\frac{1}{5}-\frac{1}{a+4}=\frac{184}{945}\)

\(\Leftrightarrow\frac{1}{a+4}=\frac{1}{5}-\frac{184}{945}\)

\(\Leftrightarrow\frac{1}{a+4}=\frac{1}{189}\)

\(\Rightarrow a+4=189\Rightarrow a=185\)